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If 5cosx+12cosy=13, then the maximum val...

If `5cosx+12cosy=13`, then the maximum value of `5sinx+12siny` is (A) `12` (B) `sqrt(120)` (C) `sqrt(20)` (D) 13

Text Solution

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`(5cosx+12cosy)=13`
`(5cosx+12cosy)^2=13^2=169`
`25cos^2x+120cosxcosy+144cos^2y=169-(1)`
`5sinx+12siny=A`
`25sin^2x+120sinxsiny+144sin^y=A^2`
adding eqution 1 and 2
25+144+120(cosxcosy+sinxsiny)
`=A^2+169`
...
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